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Andrew Schumann [51]Andrew N. Schumann [1]
  1.  22
    On the Origin of Indian Logic from the Viewpoint of the Pāli Canon.Andrew Schumann - 2019 - Logica Universalis 13 (3):347-393.
    In this paper, I show that in the Pāli Canon there was a tradition of Buddhist logic, but this tradition was weak, and the proto-logic we can reconstruct on the basis of the early Pāli texts can be evaluated as a predecessor of the Hindu logic. According to the textual analysis of the Pāli texts, we can claim that at the time of the closing of the Pāli Canon there did not exist the Nyāya philosophy known by the Nyāya Sūtra. (...)
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  2.  45
    Nāgārjunian-Yogācārian Modal Logic versus Aristotelian Modal Logic.Andrew Schumann - 2021 - Journal of Indian Philosophy 49 (3):467-498.
    There are two different modal logics: the logic T assuming contingency and the logic K = assuming logical determinism. In the paper, I show that the Aristotelian treatise On Interpretation has introduced some modal-logical relationships which correspond to T. In this logic, it is supposed that there are contingent events. The Nāgārjunian treatise Īśvara-kartṛtva-nirākṛtiḥ-viṣṇoḥ-ekakartṛtva-nirākaraṇa has introduced some modal-logical relationships which correspond to K =. In this logic, it is supposed that there is a logical determinism: each event happens necessarily or (...)
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  3. Fichte’s Formal Logic.Jens Lemanski & Andrew Schumann - 2023 - Synthese 202 (1):1-27.
    Fichte’s Foundations of the Entire Wissenschaftslehre 1794 is one of the most fundamental books in classical German philosophy. The use of laws of thought to establish foundational principles of transcendental philosophy was groundbreaking in the late eighteenth and early nineteenth century and is still crucial for many areas of theoretical philosophy and logic in general today. Nevertheless, contemporaries have already noted that Fichte’s derivation of foundational principles from the law of identity is problematic, since Fichte lacked the tools to correctly (...)
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  4.  29
    Logic, Spatial Algorithms and Visual Reasoning.Andrew Schumann & Jens Lemanski - 2022 - Logica Universalis 16 (4):535-543.
    Spatial and diagrammatic reasoning is a significant part not only of logical abilities, but also of logical studies. The authors of this paper consider some novel trends in studying this type of reasoning. They show that there are the following two main trends in spatial logic: (i) logical studies of the distribution of various objects in space (logic of geometry, logic of colors, etc.); (ii) logical studies of the space algorithms applied by nature itself (logic of swarms, logic of fungi (...)
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  5.  24
    Non-Archimedean fuzzy and probability logic.Andrew Schumann - 2008 - Journal of Applied Non-Classical Logics 18 (1):29-48.
    In this paper the non-Archimedean multiple-validity is proposed for basic fuzzy logic BL∀∞ that is built as an ω-order extension of the logic BL∀. Probabilities are defined on the class of fuzzy subsets and, as a result, for the first time the non-Archimedean valued probability logic is constructed on the base of BL∀∞.
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  6.  34
    Preface.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):1-8.
    In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa-omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.
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  7.  21
    Syllogistic System for the Propagation of Parasites. The Case of Schistosomatidae.Andrew Schumann & Ludmila Akimova - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):303-319.
    In the paper, a new syllogistic system is built up. This system simulates a massive-parallel behavior in the propagation of collectives of parasites. In particular, this system simulates the behavior of collectives of trematode larvae.
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  8. Non-well-foundedness in Judaic Logic.Andrew Schumann - 2008 - Studies in Logic, Grammar and Rhetoric 13 (26).
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  9. Reflection in Scientific Activity and Hierarchical Model of Argumentation.Mary Dziśko & Andrew Schumann - 2008 - Studies in Logic, Grammar and Rhetoric 13 (26).
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  10.  66
    Logical Cornestones of Judaic Argumentation Theory.Andrew Schumann - 2013 - Argumentation 27 (3):305-326.
    In this paper, the four Judaic inference rules: qal wa- ḥ omer, gezerah š awah, heqe š, binyan ’av are considered from the logical point of view and the pragmatic limits of applying these rules are symbolic-logically explicated. According to the Talmudic sages, on the one hand, after applying some inference rules we cannot apply other inference rules. These rules are weak. On the other hand, there are rules after which we can apply any other. These rules are strong. This (...)
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  11.  7
    Sign-inferences in Greek and Buddhist Logic.Andrew Schumann - forthcoming - History and Philosophy of Logic:1-33.
    The Yogācāra school of logic developed a theory of sign-inferences that has many features of the Stoic and Epicurean logical teachings with small inclusions of Aristotelian ideas. In the Nyāyabindu of Dharmakīrti, we can find the following schemes of formal reasoning: modus Barbara (Figure I) and modus Camenes (Figure IV) of the Aristotelian syllogistic, and all the inference rules of the Stoic logic: modus ponens, modus tollens, modus ponendo tollens, modus tollendo ponens I, modus tollendo ponens II. The three premises (...)
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  12.  53
    A lattice for the language of Aristotle's syllogistic and a lattice for the language of Vasiľév's syllogistic.Andrew Schumann - 2006 - Logic and Logical Philosophy 15 (1):17-37.
    In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľév’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on cap-semilattice and a lattice for the language of Vasiľév’s syllogistic is called a vectorial lattice on closure cap-semilattice. These constructions are introduced for the first time.
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  13.  6
    Judaic logic.Andrew Schumann (ed.) - 2010 - Piscataway, NJ: Gorgias Press.
    Judaic reasoning is discussed from the standpoint of modern logic. Andrew Schumann defines Judaic logic, traces Aristotelian influence on developing Jewish studies in Judaic reasoning, and shows the non-Aristotelian core of fundamentals of Judaic logic. Further, Schumann proposes some modern approaches to understanding and formalizing Judaic reasoning, including Judaic semantics and (non-Aristotelian) syllogistics.
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  14.  3
    Logic in Religious Discourse.Andrew Schumann (ed.) - 2010 - De Gruyter.
    Knocking on Heaven's Door is the oldest human dream that seems unrealized still. Religious discourse does show the road, but it requires a blind faith in return. In this book logicians try to hear Heaven's Call and to analyze religious discourse. As a result, the notion of religious logic as a part of philosophical logic is introduced. Its tasks are (1) to construct consistent logical systems formalizing religious reasoning that at first sight seems inconsistent (this research is fulfilled within the (...)
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  15.  21
    Physarum Polycephalum Syllogistic L-Systems and Judaic Roots of Unconventional Computing.Andrew Schumann - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):181-201.
    We show that in Kabbalah, the esoteric teaching of Judaism, there were developed ideas of unconventional automata in which operations over characters of the Hebrew alphabet can simulate all real processes producing appropriate strings in accordance with some algorithms. These ideas may be used now in a syllogistic extension of Lindenmayer systems, where we deal also with strings in the Kabbalistic-Leibnizean meaning. This extension is illustrated by the behavior of Physarum polycephalum plasmodia which can implement, first, the Aristotelian syllogistic and, (...)
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  16.  13
    p-Adic valued logical calculi in simulations of the slime mould behaviour.Andrew Schumann - 2015 - Journal of Applied Non-Classical Logics 25 (2):125-139.
    In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould, the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than attractants, then this behaviour can be coded in terms of p-adic numbers. As a result, this (...)
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  17.  1
    The Swarm Computing Approach to Business Intelligence.Andrew Schumann, Krzysztof Pancerz & Andrzej Szelc - 2015 - Studia Humana 4 (3):41-50.
    We have proposed to use some features of swarm behaviours in modelling business processes. Due to these features we deal with a propagation of business processes in all accessible directions. This propagation is involved into our formalization instead of communicating sequential processes. As a result, we have constructed a business process diagram language based on the swarm behavior and an extension of that language in the form of reflexive management language.
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  18.  10
    The Traditional Approach to the Periodization of Indian Philosophy as a Hegelian Approach.Andrew Schumann - 2023 - Studia Humana 12 (3):32-41.
    This paper is devoted to the methodology of history of philosophy. There are considered two approaches: the Hegelian and Schellingian ones. It is shown that the Hegelian approach has many weak points. Both approaches are demonstrated on the material of Indian philosophy. The Schellingian approach was hammered out then by Foucault as archeology of philosophy.
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  19.  26
    On the Origin of Logical Determinism in Babylonia.Andrew Schumann - 2021 - Logica Universalis 15 (3):331-357.
    In this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal (...)
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  20. Cyclic Proofs in Argumentation. The Case of Excluding Boris Pasternak from the Assoication of Writers in the USSR.Mary Dziśko & Andrew Schumann - 2009 - Studies in Logic, Grammar and Rhetoric 16 (29).
     
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  21.  10
    The Logic System is the Way You Do Logic.Dov M. Gabbay & Andrew Schumann - 2014 - Studia Humana 3 (4):41-44.
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  22.  20
    Logical Approach to p-adic Probabilities.A. Yu Khrennikov & Andrew Schumann - 2006 - Bulletin of the Section of Logic 35 (1):49-57.
  23.  12
    Brain and Its Universal Logical Model of Multi-Agent Biological Systems.Jerzy Król, Andrew Schumann & Krzysztof Bielas - 2022 - Logica Universalis 16 (4):671-687.
    We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as _Physarum polycephalum_, bacterial colonies or any other swarm), reacting to external nourishment stimuli. Our construction follows the topological description of brain activity, where particles (neurons) are activated by an external environment, represented by a topological space _X_ with an open cover \(\{U_i:i\in I\}\). The brain builds the model of this external space via the nerve (trace) of a topological space _X_. Here the body of _Physarum (...)
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  24.  2
    The Formal Layer of {Brain and Mind} and Emerging Consciousness in Physical Systems.Jerzy Król & Andrew Schumann - forthcoming - Foundations of Science:1-30.
    We consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised (...)
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  25.  3
    Defining a Me th=11pt ṇḍ th aka Question in the Questions of Milinda and Its Commentarial Texts.Eng Jin Ooi, Andrew Schumann & Natchapol Sirisawad - 2023 - Journal of Indian Philosophy 51 (5):567-589.
    The word _meṇḍaka_, a derivative of _meṇḍa_ (“ram”), is generally translated as “made of the ram” or “about the ram” or “horned.” However, in the Pāli _Milindapañha_ (_Questions of Milinda_), the word _meṇḍakapañha_, literally, a question about the ram, is also rendered as a logical conclusion that refutes an imaginary dilemma. Hence, in this treatise, the word _meṇḍaka_ is a special logical term which means an imaginary dilemma that can be logically refuted. This raises the question as to why the (...)
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  26.  5
    Logic in Central and Eastern Europe: History, Science, and Discourse.Andrew Schumann (ed.) - 2012 - Lanham, Md.: Rowman & Littlefield.
    This book is a collection of rare material regarding logical and analytic-philosophical traditions in Central and Eastern European countries, covering the period from the late nineteenth century to the early twenty-first century. An encyclopedic feature covers the history of logic and analytic philosophy in all European post-Socialist countries.
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  27. A Novel Tendency in Philosophical Logic.Andrew Schumann - 2008 - Studies in Logic, Grammar and Rhetoric 14 (27).
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  28. Circular Proofs in Proof-theoretic Simulation of Belousov-Zhabotinsky Reaction.Andrew Schumann - 2009 - Studies in Logic, Grammar and Rhetoric 17 (30).
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  29.  4
    Creative Reasoning and Content-Genetic Logic.Andrew Schumann - 2018 - Studia Humana 7 (4):39-47.
    In decision making quite often we face permanently changeable and potentially infinite databases when we cannot apply conventional algorithms for choosing a solution. A decision process on infinite databases is called troubleshooting. A decision on these databases is called creative reasoning. One of the first heuristic semi-logical means for creative decision making were proposed in the theory of inventive problem solving by Genrich Altshuller. In this paper, I show that his approach corresponds to the so-called content-generic logic established by Soviet (...)
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  30.  9
    Judgments and Truth: Essays in Honour of Jan Woleński.Andrew Schumann - 2020 - Studia Humana 9 (3-4):1-9.
    It is a Preface to Volume 9:3/4 that has brought a renewed focus to the role of truth conceptions in frameworks of semantics and logic. Jan Woleński is known due to his works on epistemological aspects of logic and his systematization of semantic truth theory. He became the successor and the worthy continuer of prominent Polish logicians: Alfred Tarski and Kazimierz Ajdukiewicz. This volume is collected on the 80th anniversary of Woleński’s birth and draws together new research papers devoted to (...)
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  31.  2
    Logical Determinacy versus Logical Contingency. The Case of Łukasiewicz’s Three-valued Logic.Andrew Schumann - 2019 - Studia Humana 8 (2):8-15.
    In constructing the three-valued logic, Jan Łukasiewicz was highly inspirited by the Aristotelian idea of logical contingency. Nevertheless, we can construct a four-valued logic for explicating the Stoic idea of logical determinacy. In this system, we have the following truth values: 0 (‘possibly false), 1 (‘necessarily false’), 2 (‘possibly true’), 3 (‘necessarily true’), where the designated truth value is represented by the two values: 2 and 3.
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  32.  2
    Logics for Physarum Chips.Andrew Schumann & Krzysztof Pancerz - 2016 - Studia Humana 5 (1):16-30.
    The paper considers main features of two groups of logics for biological devices, called Physarum Chips, based on the plasmodium. Let us recall that the plasmodium is a single cell with many diploid nuclei. It propagates networks by growing pseudopodia to connect scattered nutrients. As a result, we deal with a kind of computing. The first group of logics for Physarum Chips formalizes the plasmodium behaviour under conditions of nutrient-poor substrate. This group can be defined as standard storage modification machines. (...)
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  33.  3
    Logic in Central and Eastern Europe: History, Science, and Discourse.Andrew Schumann (ed.) - 2012 - Lanham, Md.: Upa.
    This book is a collection of rare material regarding logical and analytic-philosophical traditions in Central and Eastern European countries, covering the period from the late nineteenth century to the early twenty-first century. An encyclopedic feature covers the history of logic and analytic philosophy in all European post-Socialist countries.
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  34.  4
    Logic in Orthodox Christian Thinking.Andrew Schumann (ed.) - 2012 - De Gruyter.
    The Orthodox Christian thought is the most modally rigorous way of inferring. The subject of the book is to investigate possibilities of explicating the Orthodox thought from the viewpoint of analytic philosophy and symbolic logic. The claim that Orthodox thinking is just mystic and illogical is not true. The logical culture of Orthodox Christian thinking is unknown and ununderstandable for the West, although its schemata are very influential in Eastern Europe till now (Marxism-Leninism is just one of their possible instances). (...)
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  35.  6
    Logical Reasoning for Forecasting in Mesopotamia.Andrew Schumann - 2021 - Studies in Logic, Grammar and Rhetoric 66 (3):721-746.
    In this paper, I show that a kind of perfect logical competence is observed in the Babylonian tablets used for forecasting. In these documents, we see an intuition of some algebraic structures that are used for inferring prognoses as logical conclusions. The paper is based mainly on the omen series reconstructed by N. De Zorzi. It is shown that in composing these divination lists there was implicitly used the Boolean algebra.
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  36.  16
    Modal Calculus of Illocutionary Logic.Andrew Schumann - 2010 - In Piotr Stalmaszczyk (ed.), Objects of Inquiry in Philosophy of Language and Linguistics. Ontos Verlag. pp. 261.
  37. Modal Calculus of Illocutionary Logic.Andrew Schumann - 2010 - In Piotr Stalmaszczyk (ed.), Philosophy of Language and Linguistics: Volume I: The Formal Turn; Volume II: The Philosophical Turn. De Gruyter. pp. 261-276.
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  38.  22
    Non-Archimedean valued predicate logic.Andrew Schumann - 2007 - Bulletin of the Section of Logic 36 (1/2):67-78.
  39.  8
    Preface: Ideas and Society on the 150th Anniversary of the Birth of Leon Petrażycki.Andrew Schumann - 2018 - Studia Humana 7 (3):3-4.
    It is a Preface to Volumes 7:3 and 7:4 consisting of articles presented at the International Interdisciplinary Conference Ideas and Society on the 150th anniversary of the birth of Leon Petrażycki, held on November 24, 2017, in Rzeszów, Poland.
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  40.  2
    Philosophical logic.Andrew Schumann (ed.) - 2008 - Białystok: University of Białystok.
  41.  4
    Preface: Philosophical Basis for Making Decisions (on the 140th Anniversary of the Birth of Jan Łukasiewicz).Andrew Schumann & Jan Woleński - 2019 - Studia Humana 8 (2):1-2.
    It is a Preface to Volume 8:2 (2019) consisting of articles presented at the International Interdisciplinary Conference anniversary of the birth of Jan Łukasiewicz, Rzeszów, Poland.
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  42.  7
    Pragmatic Studies in Judaism.Andrew Schumann, Aviram Ravitsky, Lenn E. Goodman, Furio Biagini, Alan Mittleman, Uri J. Schild, Michael Abraham, Dov Gabbay, Peter Ochs, Yuval Jobani & Tzvee Zahavy (eds.) - 2013 - Piscataway, NJ: Gorgias Press.
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  43.  32
    Qal wa- omer and Theory of Massive-Parallel Proofs.Andrew Schumann - 2011 - History and Philosophy of Logic 32 (1):71-83.
    In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa- omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.
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  44.  8
    Reflexive Games in Management.Andrew Schumann - 2018 - Studia Humana 7 (1):44-52.
    In this paper reflexive games are defined as a way to act beyond equilibria to control our opponents by our hiding motives. The task of a reflexive game is to have the opponent’s actions become transparent for us, while our actions remain obscure for the competitor. In case a reflexive game is carried out between agents belonging to the same organisation, success in a reflexive game can be reached by a purposeful modification of some components of a controlled system. Such (...)
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  45.  6
    Stoic Roots of Orthodox Christian Thinking.Andrew Schumann - 2012 - In Logic in Orthodox Christian Thinking. De Gruyter. pp. 204-229.
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  46. The Baba Qama from the logical point of view.Andrew Schumann - 2013 - In Jan Woleński, Yaron M. Senderowicz & Józef Bremer (eds.), Jewish and Polish philosophy. Austeria Publishing House.
     
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  47.  2
    Trends in Argumentation Logic.Andrew Schumann, Elena Lisanyuk & Sofia Almpani - 2022 - Studia Humana 11 (3-4):1-5.
    In this paper, we introduce the subject of the special issue Trends in Argumentation Logic. Here we mainly describe two approaches to argumentation logic with explicating monotonic and non-monotonic, or defeasible, reasoning and explain the role of artificial intelligence in applying argumentation logic. Then we give a short overview of the papers contributed to the special issue.
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  48.  1
    The Milindapañha in the Context of History of Indian Civilization.Andrew N. Schumann - 2020 - RUDN Journal of Philosophy 24 (4):544-569.
    This paper restores the historical context of Milindapaha. The text is unique, because it is one of the very few documents of Ancient India, in which one of the authors is considered a Greek as a participant in the dialog. To reconstruct the context of the book, the basic archeological data about the Indo-Greek Kingdom, including epigraphics, are summed up, as well as there are analyzed some references to the kingdom given in the Mahāvaṃsa, the earliest chronicle of Sri Lanka. (...)
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  49. Unconventional Probabilities and Fuzziness in CADIAG's Computer-Assisted Medical Expert Systems.Andrew Schumann - 2010 - Studies in Logic, Grammar and Rhetoric 22 (35).
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  50.  28
    Towards New Probabilistic Assumptions in Business Intelligence.Andrzej Szelc & Andrew Schumann - 2014 - Studia Humana 3 (4):11-21.
    One of the main assumptions of mathematical tools in science is represented by the idea of measurability and additivity of reality. For discovering the physical universe additive measures such as mass, force, energy, temperature, etc. are used. Economics and conventional business intelligence try to continue this empiricist tradition and in statistical and econometric tools they appeal only to the measurable aspects of reality. However, a lot of important variables of economic systems cannot be observable and additive in principle. These variables (...)
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